# Average Curvature FISTA for Nonconvex Smooth Composite Optimization Problems

arXiv: https://arxiv.org/abs/2105.06436 · HTML: https://mlsanity.com/paper/2105.06436/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 May 2021.

## Built on by (most cited first, 1 of 1)

- [Projected gradient methods for nonconvex and stochastic smooth optimization: new complexities and auto-conditioned stepsizes](https://mlsanity.com/paper/2412.14291/) (2024)

## Abstract (arXiv)

A previous authors' paper introduces an accelerated composite gradient (ACG) variant, namely AC-ACG, for solving nonconvex smooth composite optimization (N-SCO) problems. In contrast to other ACG variants, AC-ACG estimates the local upper curvature of the N-SCO problem by using the average of the observed upper-Lipschitz curvatures obtained during the previous iterations, and uses this estimation and two composite resolvent evaluations to compute the next iterate. This paper presents an alternative FISTA-type ACG variant, namely AC-FISTA, which has the following additional features: i) it performs an average of one composite resolvent evaluation per iteration; and ii) it estimates the local upper curvature by using the average of the previously observed upper (instead of upper-Lipschitz) curvatures. These two properties acting together yield a practical AC-FISTA variant which substantially outperforms earlier ACG variants, including the AC-ACG variants discussed in the aforementioned authors' paper.